Is artificial intelligence and, in particular, neural networks being used in real-world critical applications?
This is as much an ethical concern as a practical one.

AI systems are already reaching or exceeding human performance in many critical areas. Consider the detection of common cancers, where AI systems match or exceed humans. Another good example is Tesla's Autopilot, which is actually safer than human drivers, but gets a lot of bad press when it makes a mistake. Both of these systems are likely using Neural Networks, possibly alongside other heuristic or rule-drive approaches.

The issue isn't whether these systems can be "safe enough" for everyday use. They are safe enough in a societal sense already. The concern is that the people who die when these systems make mistakes are randomly selected, whereas the people who die when a human performs the work die because a human makes a mistake (usually). This is difficult to accept for the same reason that some people are scared of flying, even though it is many times safer than driving the same distance: there is a loss of control, and "good" people may die through no fault of their own, or perhaps through events that are no one's fault.

Whether we use this systems will thus probably depend on the application. In Medicine it's easy to see a case: we can do more tests than before for the same price. People who can afford to have a doctor review the machine's decisions are probably no worse off. People who couldn't afford this already are better off (they get a diagnosis with some positive predictive power value now, instead of none at all). In driving, it's more complicated, and will probably require further development. No one knows for sure how good self-driving cars can get, but they'll probably get somewhat better over time. Maybe they'll get good enough that they more or less never kill people, or maybe they won't.

I actually think your friend is way off about the use cases he thinks AI is not suitable for though. Check out this article in Military Embedded Systems. In applications where decisions are made on a pure cost/benefit basis (and not based on people's gut feelings about morality), AI systems are actually easier to adopt, and are already often better than human operators. This trend seems likely to increase in the future, so "technical devices and sensors", which are often black-boxes to the lay public anyway, seem like they are among the first things to go.